Resource-bounded discoverability of quantum circuits

Determine how much computationally powerful quantum circuits can be reached by a resource-bounded learning, search, or design process using only the information supplied by a task, and characterize how the available task information and discovery resources determine the reachable portion of circuit space.

Background

The paper develops a mixed discrete–continuous representation of variational quantum circuits in which CNOT routing matrices determine both global representational capacity and local tangent accessibility. Although a useful circuit may have a compact description, the space of possible routing tuples is exponentially large, so representing or implementing a circuit is distinct from discovering one from task feedback.

The proposed same-point routing augmentation provides a local mechanism for opening new descent directions while preserving the current unitary, state, loss, and existing gradients. However, the paper does not establish an efficient global discovery procedure or determine the broader boundary between circuits that are computationally powerful in principle and circuits that can actually be found under finite information and resource constraints. The unresolved problem therefore concerns the reachability of useful quantum circuits by resource-bounded discovery processes.